Absolutely convergent series expansions for quasi periodic motions.

Abstract

this paper we shall describe the Lindstedt series together with a natural quasi-periodic series expansion, and we shall explain why it is absolutely divergent. We shall then describe a large class of compensations for the terms in the series expansion, and by taking into account these compensations, we shall obtain new quasi-periodic series which are absolutely convergent. This we shall prove by generalizing Siegel's method